Perception & Psychophysics
1996, 58 (6), 927–935
Memory for musical tempo: Additional evidence
that auditory memory is absolute
DANIEL J. LEVITIN
University of Oregon, Eugene, Oregon
and Stanford University, Stanford, California
and
PERRY R. COOK
Stanford University, Stanford, California
We report evidence that long-term memory retains absolute (accurate) features of perceptual
events. Specifically, we show that memory for music seems to preserve the absolute tempo of the
musical performance. In Experiment 1, 46 subjects sang two different popular songs from memory,
and their tempos were compared with recorded versions of the songs. Seventy-two percent of the
productions on two consecutive trials came within 8% of the actual tempo, demonstrating accuracy
near the perceptual threshold (JND) for tempo. In Experiment 2, a control experiment, we found
that folk songs lacking a tempo standard generally have a large variability in tempo; this counters arguments that memory for the tempo of remembered songs is driven by articulatory constraints. The
relevance of the present findings to theories of perceptual memory and memory for music is discussed.
A fundamental problem facing memory theorists is
how to account for two seemingly disparate properties of
memory. On the one hand, a rich body of literature suggests that the role of memory is to preserve the gist of
experiences; memory functions to formulate general rules
and create abstract concepts on the basis of specific exemplars (Posner & Keele, 1970; Rosch, 1975). On the other
hand, there is the extensive literature suggesting that
memory accurately preserves absolute features of experiences (Brooks, 1978; Jacoby, 1983; Medin & Schaffer,
1978). (For a further discussion of these two perspectives, see McClelland & Rumelhart, 1986.)
These perspectives on the function of human memory
parallel an old debate in the animal-learning literature
about whether animals’ internal representations are relational or absolute (Hanson, 1959; Reese, 1968). As with
This research was supported by a National Defense Science and
Engineering Graduate Fellowship to the first author, and by NSF Research Grant BNS 85-11685 to R. N. Shepard. This report was prepared in part while the first author was a Visiting Research Fellow at
the Center for Computer Research in Music and Acoustics, Stanford
University, Winter 1994–1995. We are grateful to the following for
their generous contributions to this work: Jamshed Bharucha, Chris
Chafe, Jay Dowling, Andrea Halpern, Stephen Handel, Douglas
Hintzman, Jay Kadis, Carol Krumhansl, Max Mathews, Joanne
Miller, Caroline Palmer, John R. Pierce, Michael Posner, Bruno Repp,
Roger Shepard, Julius Smith, the researchers and staff of CCRMA,
and especially Malcolm Slaney and the participants in the weekly
CCRMA Hearing Seminar. Any errors remaining in this work were
probably pointed out to us by these people, but we were too stubborn
to change them. Correspondence may be sent to D. J. Levitin, Department of Psychology 1227, University of Oregon, Eugene, OR
97403-1227 (e-mail: levitin@cogsci.uoregon.edu). P. R. Cook is now
at the Department of Computer Science, Princeton University.
many psychological debates, there may be some degree
of truth on both sides. Currently, philosophers of mind
(Dennett, 1991) and cognitive scientists (Kosslyn, 1980)
have also wondered to what extent our mental representations and memories of the world are perfect or accurate
copies of experience, and to what extent distortions (or
generalizations) intrude.
The study of memory for music is potentially helpful
in exploring these issues because the experimental evidence is that both relational and absolute features of
music are encoded in memory. Researchers have shown
that people have little trouble recognizing melodies
transposed in pitch (Attneave & Olson, 1971; Dowling
& Bartlett, 1981), so it is clear that memory for musical
melody must encode the abstract information—that is,
the relation of successive pitches, or pattern of tones if
not their actual location in pitch space.
Abstract encoding has also been demonstrated for
temporal features: people easily recognize songs in which
the relation between rhythmic elements (the rhythmic
pattern) is held constant but the overall timing or musical tempo has been changed (Monahan, 1993; Serafine,
1979). (We define tempo as the “pace” of a musical piece:
measured as the amount of time it takes for a given note,
or the average number of beats occurring in a given interval of time, usually beats per minute.)
With respect to this point about musical relations,
Hulse and Page (1988) explain,
music emphasizes the constancy of relations among
sounds . . . within temporal structure, music emphasizes
the constancy of relations among tone durations and intertone intervals. Rhythmic structures remain perceptually equivalent over a broad range of tempos . . . and tempo
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Copyright 1996 Psychonomic Society, Inc.
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LEVITIN AND COOK
changes involve ratio changes of duration and interval.
(p. 431)
And, as Monahan (1993) argues, musical pitch and
time are described most naturally in relative rather than
absolute terms. Thus (within very broad limits), the identity and recognizability of a song are maintained through
transposition of pitch and changes in tempo.
Evidence that memory for music also retains absolute
pitch information alongside an abstract melody representation has been mounting for some time (Deutsch,
1991; Halpern, 1989; Levitin, 1994; Lockhead & Byrd,
1981; Terhardt & Seewann, 1983). For example, in a previous study, one of us (Levitin, 1994) asked experimental subjects (most of them nonmusicians) to sing their favorite rock and roll songs from memory, without any
external reference. When the tones of the subjects’ productions were compared with the tones of the recorded
songs, they were found to be at or very near the songs’ actual pitches. This is somewhat surprising from the standpoint of music theory (and perhaps from “object perception” theories), because that which gives a melody its
identity or “objectness” is the relation of successive intervals (both rhythmic and melodic). As most music theorists would agree, “music places little emphasis on the
absolute properties of sounds, such as their exact temporal pitch or duration” (Hulse & Page, 1988, p. 432).
The animal learning literature reveals parallel evidence for both absolute and relational memory for auditory stimuli. Starlings (Hulse & Page, 1988) and whitethroated sparrows (Hurly, Ratcliffe, & Weisman, 1990)
were shown to use both absolute and relative pitch information in discriminating melodies, but other evidence
is mixed. Barn owls seem to remember musical patterns
on the basis of absolute pitch (Konishi & Kenuk, 1975),
and wolves use absolute pitch information to the exclusion of relative pitch information to differentiate between familiar and unfamiliar howls (Tooze, Harrington,
& Fentress, 1990).
What reasons are there to expect that long-term memory might encode tempo information with a high degree
of accuracy? Scores of conditioning experiments with
animals have shown that animals can learn to estimate
interval durations with great accuracy (Hulse, Fowler, &
Honig, 1978).
The question of human memory for tempo has been
addressed in several key studies. People report that their
auditory images seem to have a specific tempo associated with them (Halpern, 1992), and in one study, subjects who imagined songs tended to imagine them at about
the same tempo on occasions separated by as much as
5 days (Halpern, 1988). Collier and Collier (1994) found
that trained jazz musicians tended to vary tempo less
than 5% within a song or across multiple performances
of the same song on different days, suggesting a stable
memory for tempo in these musicians.
Whereas the studies just mentioned argue for the stability of internal tempos, the question of the objective ac-
curacy of these internal tempos interested us. That is,
when we remember a song (or “auralize” it, to use W. D.
Ward’s terminology) do we do so at its original tempo?
Just as some people can match pitches accurately (and
we say they have “absolute pitch”), we wondered whether
there are those who can match tempos accurately and
have an ability of “absolute tempo.” In particular, we
wanted to study this ability in everyday people with little formal musical training. This question is relevant to
researchers studying human rhythm perception (e.g., Desain, 1992; Jones & Boltz, 1989; Povel & Essens, 1985;
Steedman, 1977), the nature and stability of internal
clocks (Collier & Wright, 1995; Collyer, Broadbent, &
Church, 1994; Helmuth & Ivry, 1996), mental imagery
(Finke, 1985; Kosslyn, 1980), and general theories of
time perception (Block, 1990; Fraisse, 1981; Michon &
Jackson, 1985).
On a music-theoretic level, Narmour (1977) argues
that musical listening involves using both schematic reduction and unreducible (absolute) idiostructural information. To the extent that the original listening experience is preserved in the brain, we might expect to find
these two types of information represented in memory,
not just in perception. One of the goals of the present
study was to test this hypothesis.
EXPERIMENT 1
Experiment 1 was designed to discover whether people encode the absolute tempo of a familiar song in memory, and if so,with what degree of precision. In Levitin
(1994), subjects were asked to sing contemporary popular and rock songs from memory, and their productions
were analyzed for pitch accuracy. Using these same data,
we analyzed their productions for tempo accuracy. Contemporary popular and rock songs form an ideal stimulus set for our study, because they are typically encountered in only one version by a particular musical artist or
group, and so the song is always heard— perhaps hundreds of times—in the same key, and at the same tempo.
(In fact, we excluded songs that did not meet this criterion.)
Method
The raw data used in this study were originally collected for a
study on pitch memory (Levitin, 1994).
Subjects. The subjects were 46 Stanford University students
who served without pay. The subjects did not know in advance
that they were participating in a study involving music, and the
sample included subjects with and without some musical background. All subjects filled out a general questionnaire before the
experimental session. The subjects ranged in age from 16 to 35
years (mean, 19.5; mode, 18; SD, 3.7).
By self-report, the subjects’ musical background ranged from
no instruction to more than 10 years of instruction; 37 subjects
had some exposure to a musical instrument, 9 had none. In response to the question “how much structured musical training in
either performance or theory have you had?” 17 subjects reported
none; 17 subjects reported 1–3 years; 5 subjects reported 3–5
MEMORY FOR TEMPO
years; 3 subjects reported 5–7 years; 3 subjects reported 7–10
years; and 1 subject reported more than 10 years.
Materials. Prior to data collection, a norming study was conducted to select stimuli with which this subject population would
be familiar. Two hundred fifty introductory psychology students
completed a questionnaire, on which they were asked to indicate
songs that “they knew well and could hear playing in their heads.”
None of the subjects in the norming study were subsequently used
in the main experiment.
The results of this norming study were used to select the best
known songs. Songs on this list that had been performed by more
than one group were excluded from the stimulus set because of the
possibility that these versions might have different tempos. From
this questionnaire, 58 compact discs (CDs) were selected, representing over 600 songs from which the subjects could choose. Examples of songs included are “Hotel California” by The Eagles;
“Get into the Groove” by Madonna; and “This & That” by
Michael Penn. (A complete list of CDs constituting the stimulus
set is available from the first author.)
Procedure. Subjects were seated in a sound attenuation booth
alongside the experimenter. The 58 CDs chosen from the norming study were displayed alphabetically on a shelf in front of the
subjects. The experimenter followed a written protocol asking
subjects to select from the shelf and to hold in their hands a CD
that contained a song they knew very well. Holding the CD and
looking at it may have provided a visual cue for subsequent auditory imaging. There was no CD player in the booth, and at no time
were the CDs actually played for the subjects. All subjects reported that they had not actually heard their chosen song in the
previous 72 h, and many had not heard it in months.
The subjects were then asked to close their eyes and imagine
that the song was actually playing. They were told that, when they
were ready, we wanted them to try to reproduce the tones of the
song by singing, humming, or whistling, and they could start anywhere in the song they wanted to. The subjects were not explicitly
told anything about rhythm or tempo, nor were they specifically
929
asked to reproduce the tempo of the songs. Their productions were
recorded on digital audio tape (DAT), so that the pitch and speed
would be accurately preserved. The subjects were not told how
much of the song to sing, but they typically sang a four-bar phrase.
Following the production of this first song, the subjects were
asked to choose another song and repeat the procedure; this constituted the two experimental trials. Three of the subjects discontinued their participation after Trial 1.
Analysis. The subjects’ productions were compared with the
songs performed by the original artists on CD, in order to compare
tempos. The subjects’ productions and the corresponding sections
of the CD were transferred digitally to a Macintosh computer, and
the sample rate was converted from its original 44.1 kHz or
48 kHz to 22.050 kHz for storage economy.
The durations of each subject’s production and the associated CD
excerpt were measured with the program MacMix, and these measurements were accurate to within 0.1 msec. A typical subject production was 5 sec long. The total selection was also divided into
beats yielding two equivalent measures of production time: total
duration and beats per minute. For the purposes of this report, data
are presented as tempos in units of beats per minute (bpm).
Results
Figure 1 shows, as a bivariate scatterplot, the tempos
produced by subjects in comparison with the actual tempos of the remembered pieces (Trials 1 and 2 are combined). The subjects came very close to their target tempos,
as is indicated by the high correlation between subjects’
tempos and actual tempos (r ⫽ .95) and the fact that most
responses fall near the diagonal. Figure 2 shows the distribution of errors that the subjects made, expressed in a
histogram as percent deviations from the actual tempo.1
On Trial 1, 33/46, or 72%, of the subjects performed
within ⫾4% of the actual tempo for the songs, and 41/46,
Figure 1. Subjects’ tempos versus actual tempos, both trials combined.
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LEVITIN AND COOK
or 89%, of the subjects performed within ⫾8% of the actual tempo (M ⫽ 4.1%; SD ⫽ 7.7%). On Trial 2, 12/42,
or 40%, of the subjects came within ⫾4%, and 25/42, or
60%, came within ⫾8% of the actual tempo (M ⫽ 7.7%;
SD ⫽ 7.9%). As Figure 2 shows, for the two trials combined, 72% of the responses fell within 8%.
To put these results in context, one might ask, what is
the JND for tempo? Drake and Botte (1993, Experiment 3) found the JND for tempo discrimination to be
6.2%–8.8% using a two-alternative forced choice listening (“which is faster?”) test; Friberg and Sundberg
(1993) found JND for tempo to be 4.5% using the psychophysical method of adjustment; Hibi (1983) found
the JND to be ~6% for displacement of a single time
marker in a sequence, and for lengthening/shortening of
a single time marker. In tapping tasks, where subjects
had to either tap along with a pulse at a certain tempo (a
“synchronization task”) or continue tapping to a tempo
set up by the experimenter (“continuation task”), JNDs
of 3%–4% have been reported for synchronization (Collyer et al., 1994; Povel, 1981), and 7%–11% for continuation (Allen, 1975). All of these JNDs apply for tempos
in the range our subjects sang. It appears, then, that a
large percentage of the subjects in our study performed
within one or two JNDs for tempo, based solely on their
memory for the musical pieces.
A somewhat more ecologically valid confirmation of
these JND figures comes from Perron (1994). In contemporary popular music, many recordings are made
with drum machines or computer sequencers instead of
live drummers. The anecdotal opinion of musicians and
record producers has been that these machines are much
more able to hold a steady tempo than are human players. Perron measured the tempo deviations in a number
of these devices and found the mean tempo deviation to
be 3.5% (with a standard deviation of 4.5%). Because
the deviations in these machines seem to go largely un-
noticed by most people (including professional drummers), it seems fair to assume that this 3.5% is less than
the JND for tempo variation. An interesting implication
of Perron’s finding is that our subjects may well have
been trying to reproduce tempos for songs that contain
variations of this magnitude.
One might ask whether the subjects in our study performed consistently across the two trials. To measure
this, trials on which the subjects came within ⫾6% were
considered “hits” and all others were considered “misses,”
in accordance with the more conservative of Drake and
Botte’s (1993) JND estimates. Twenty-five subjects (or
60%) were found to be consistent in their performance
across trials. Yule’s Q was computed as a measure of
strength of association for this 2 ⫻ 2 table, and was significant (Q ⫽ .50; p < .04).
Next, we wondered whether the subjects who had accurate tempo memory also had accurate pitch memory
(as measured in Levitin, 1994). Combining Trials 1 and
2, and using 6% as a “hit” criterion for tempo and ⫾1
semitone (s.t.) as a criterion for pitch, we did not find a
significant association (Yule’s Q ⫽ .31; n.s.).2
One of the implicit assumptions in these analyses is
that the tempos of the songs that our subjects sang were
widely distributed. If all the songs fell into a narrow
tempo band, one might argue that the subjects had memory for only a particular tempo (or narrow set of tempos).
As Figure 1 shows, however, the range of tempos produced by subjects was very large, running from approximately 60 bpm to over 160 bpm.
Similarly, one might wonder whether the good performance of subjects across trials was merely due to all of
the subjects’ singing songs at the same tempo in both
cases; individual subjects may have an idiosyncratic
“preferred” tempo (or “internal tempo”) that they knew
well and relied on for this task (Braun, 1927). We found
that the correlation between tempos sung on Trial 1 and
Figure 2. Percent deviation from actual tempo, both trials combined.
MEMORY FOR TEMPO
Trial 2 was very low (r ⫽ .07), as was the correlation between “targets” on Trial 1 and Trial 2 (the tempos subjects were trying to reproduce; r ⫽ .04).
Variations of ⫾5% during the subjects’ learning of the
material could have occurred if subjects had heard the
songs repeatedly on a cassette player or record player
that did not keep accurate speed; CD players are not subject to speed fluctuations. In one item on the questionnaire, the subjects were asked about whether they had
heard their chosen song on CD, radio, cassette, or record
player, and no correlation was found between the source
of the learning and their performance (all the commercial radio stations in the area of the study were broadcasting CDs exclusively during the study period, so
“radio” responses were considered to be “CD learning”).
Similarly no correlation was found between other factors
such as sex, age, handedness, or musical training.
Discussion
The finding that 89% of the Trial 1 subjects and 60%
of the Trial 2 subjects made errors of only ⫾8% is evidence that long-term memory for tempo is very accurate
and is near the discrimination threshold (as measured by
JNDs) for variability in tempo. These results may even
underestimate the strength of tempo memory, because
our subjects were only instructed to reproduce pitches
accurately; to the extent that they also reproduced tempo,
they did this on their own, without being requested by
the experimenter to do so.
The distribution of errors is also instructive. As Figures 1 and 2 show, there is a tight clustering near the actual tempo, and more subjects sang too fast than too
slow. Boltz (1994) reviews evidence that various forms
of induced stress increase the internal tempo of individuals. This would create internal durations that are shorter
than the standard and would cause the subjects to sing
fast. If we can assume that the experimental situation
was somewhat stressful (many subjects seemed to be
embarrassed or nervous), this could account for the
asymmetric error distribution favoring faster reproductions. An additional explanation for this asymmetry
comes from experimental findings that people are more
likely to perform faster rather than slower (Kuhn, 1977)
and are better able to detect tempo decreases rather than
increases (Kuhn, 1974).
In spite of the certain awkwardness of being asked to
sing for a psychological experiment and the concomitant
desire to be done with the task as quickly as possible,
most subjects reproduced the tempo of their selected
songs with remarkable accuracy. In listening to the subjects’ productions and to the corresponding artists’ renditions, we were struck by how close the subjects came
not just in tempo, but in pitch, phrasing, and stylistic nuances while singing from memory. In many cases, it
seemed that the subjects could not have performed better if they were actually singing along with the CD—but
of course, they were merely singing along with a representation of the CD in their heads.
931
One could argue that our findings are the result of an
artifact rather than actual “memory for tempo.” While
recalling these musical pieces, the subjects sing or imagine lyrics, and perhaps the lyrics provide a constraint for
the tempo. That is to say, the tempo of a piece might be
constrained by the number of syllables that have to be fit
into a particular melody. To counter this argument, one
would need to find a piece of music with lyrics that had
no well-defined tempo standard and ask subjects to sing
it. If the range of tempos produced for such a song is
much wider than the range produced by our subjects, we
could argue that articulatory constraints do not account
for memory for tempo.
As a first look at this issue, we examined Halpern’s
(1988) data. In her Experiment 1, Halpern asked subjects
to imagine popular songs and set a metronome to match
the tempo that they heard in their heads. Most of the
songs had the property that no single reference (or
canonical) version existed—for example, “Happy Birthday,” “London Bridge is Falling Down,” and “Twinkle,
Twinkle, Little Star.” In general, peoples’ exposure to
these songs occurs through informal live singing (such
as in elementary school), and the variety of recorded versions of these songs virtually ensures that there is no uniformly “correct” tempo. Halpern provided us with the
(previously unpublished) standard deviations across subjects for these three songs, and they were (respectively)
16%, 19%, and 22% (see Table 1).
In a replication (Experiment 2), Halpern (1988) asked
a second group of subjects to perform the same task. The
mean tempo (across subjects) for each song varied by a
large amount from one experiment to the other: for the
three songs (respectively), the differences in mean tempos were 19%, 12%, and 14%. Halpern also asked her
Experiment 2 subjects to adjust a metronome incrementally to the point that represented the fastest and slowest
that they could imagine the song to be. As Table 1 indicates, the tempos selected by the subjects varied more
than 250%. All of Halpern’s tempo variations are larger
than those we found in our subjects, supporting our
claim that the tempo was not tightly constrained by the
lyrics.
As a control condition, we designed Experiment 2 in
order to replicate Halpern’s (1988) earlier findings about
tempo variability in a production context. We recruited
8 subjects and asked them to sing three familiar folk
songs (mentioning nothing to them about tempo), and afterward to sing them as fast and slow as possible. A large
standard deviation in this task would replicate Halpern’s
finding and indicate that lyrics do not significantly constrain tempo.
EXPERIMENT 2
Method
Subjects. The subjects were 4 University of Oregon students,
and 4 members of the community, recruited without regard to musical training; 6 subjects had no previous musical instruction, 2
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LEVITIN AND COOK
Table 1
Song Tempos From Halpern (1988)
Experiment 1
Experiment 2
Fast to Slow
Title
M
SD
Experiment 2
% Difference
Fast
Slow
Difference
“Happy Birthday”
101
16%
120
19%
163
65
251%
“London Bridge”
101
19%
113
12%
170
65
262%
“Twinkle Twinkle”
99
22%
113
14%
168
63
267%
Note—Tempos are given in beats per minute. % Difference is for Experiment 1 minus Experiment 2.
Adapted, with permission, from “Perceived and Imagined Tempos of Familiar Songs,” by A. R. Halpern,
1988, Music Perception, 6, p. 198. Copyright 1988 by the Regents of the University of California. This
table also includes new, previously unpublished information supplied by the author, as well as our own
analyses of the data.
subjects had less than 2 years of musical instruction. All the subjects served without pay.
Materials. To investigate tempo variability in singing, the subjects were asked to sing “Happy Birthday,” “We Wish You A
Merry Christmas,” and “Row, Row, Row Your Boat.”
Procedure. The subjects were asked to sing one of the three
songs (song order was randomized). When they finished, they
were next asked to sing it “as slow as you possibly can” and then
“as fast as you possibly can.” This was repeated for the other two
songs. The subjects were recorded either directly to the hard disk
of a NeXT computer using the program SoundEditor, or to a Sony
DATMAN digital audio tape recorder which was then transferred
digitally to NeXTcomputer sound files.
Results
Table 2 shows the distribution of tempos for the three
songs sung at their normal speeds. The standard deviations are all well above the ~8% standard deviation that
we found for our Experiment 1 subjects. An F test between the variance in Experiment 1 and the lowest of the
Experiment 2 variances (for “Row, Row, Row Your Boat”)
confirmed that the variances were significantly different
[F(1,7) ⫽ 24.83, p < .01], using Levene’s test for homogenity of variances, and Satterthwaite’s correction for
unequal n (Snedecor & Cochran, 1989).
Figure 3 shows the variability of tempos expressed as
percent deviation from each song’s mean tempo. When
compared with Figure 2, the greater variability in tempos
is easy to see. This replicates Halpern’s (1988) finding
that production variability on these types of songs is
large. Furthermore, the fast and slow performances of
each of the three songs showed that there is indeed a
large range over which people can produce familiar
songs with lyrics. The song “Happy Birthday” exhibited
maxima and minima of 421 and 48 bpm (with the mean
across subjects being 284 and 76 bpm). “We Wish You A
Merry Christmas” exhibited maxima and minima of 129
and 22 (with means of 102 and 36). “Row, Row, Row
Table 2
Means and Standard Deviations for Experiment 2
M
SD
SD
Song Title
(bpm) (bpm) (as percent)
“Happy Birthday”
137
29.1
21%
“We Wish You A Merry Christmas”
63
11.7
18%
“Row, Row, Row Your Boat”
134
16.2
12%
Your Boat” exhibited maxima and minima of 280 and 41
(with means of 226 and 72). This large deviation in “normal” speeds, coupled with the large range of possible
speeds, confirms that a given song can be sung across a
very broad range of tempos, and that lyric or articulatory
constraints were probably not playing a role in our Experiment 1 subjects’ accurate memory for tempo.
Discussion
In Experiment 2, we replicated Halpern’s (1988) finding that the variability in tempos for popular songs that
lack a tempo standard is in the 10%–20% range, well exceeding the variability of our Experiment 1 subjects. The
accurate performance in Experiment 1 does not seem to
have been due to constraints imposed by lyrics.
GENERAL DISCUSSION
Songs contain both pitch and tempo information during their performance. What can we say about the mental representation of songs in the brain? Drake and Botte
(1993) argued for the existence of a single brain mechanism that judges the tempo of sequences (not merely the
durations of intervallic events). Judgment of tempos
might be controlled by a central timing mechanism located in the cerebellum (Helmuth & Ivry, 1996), the operation of which is based on oscillatory processes (Ivry
& Hazeltine, 1995). Such an “internal clock” may not
keep perfect time, but be subject to 1/f noise (Gilden,
Thornton, & Mallon, 1995). But pitch perception seems
to occur in brain systems separate from time perception,
beginning with frequency-selective cells in the cochlea,
all the way through to the auditory cortex (Moore &
Glasberg, 1986). So it would seem that the perception of
pitch and tempo is handled by different systems.
But memory for songs may somehow combine or link
pitch and tempo representations. Our intuition—despite
the finding that there was not a statistically significant
correlation between tempo memory and pitch memory—is that the entire spectral–temporal profile of a
song is encoded in memory in some fashion and that repeated listenings strengthen the trace. Pitt (1995) provided evidence for a central representation of instrumental timbre, which supports the notion that memory
preserves a complex, spectral–temporal image.
MEMORY FOR TEMPO
933
Figure 3. Distribution of tempos in Experiment 2. For “Happy Birthday,” SD ⫽ 21%; for “We Wish You A Merry Christmas,”
SD ⫽ 18%; for “Row, Row, Row Your Boat,” SD ⫽ 12%.
In any event, it seems increasingly clear that human
memory encodes both the absolute and the relative information contained in musical pieces, and that people are
able to access whichever is required by the given task.
This supports previous theoretical predictions that memory does encode absolute features of the original stimulus, along with abstract relations (Bower, 1967; Hintzman, 1986). This would also account for peoples’ ability
to easily recognize songs in transposition and for our
findings of their being able to reproduce a particular absolute feature. Premack (1978) offers an account of the
relation between abstract and absolute memory, suggesting that abstraction is induced only as a response to an
overburdened memory; that is, only absolute cues are
memorized until memory becomes taxed, and then the
organism forms an abstract rule.
Some colleagues have wondered whether our results
are merely the effect of “overlearning” of the stimuli,
and they have suggested that our findings are nothing
more than a measure of how well the stimuli were
learned. But we agree with Palmer (S. E. Palmer, personal communication, October 1994), who argues that increased learning is just a matter of increasing the signalto-noise ratio in memory retrieval. To toss aside the
present findings as “merely overlearning” is to miss our
point; to paraphrase Halpern (1992), we are interested in
the nature of what is encoded in memory when memory
is working well. Overlearned or well-learned stimuli
provide the cleanest measure of this.
It is well established, at least anecdotally, that expert
musicians are capable of producing tempos from memory with great accuracy. In the present study, we found
that even nonmusicians have an accurate representation
of tempo that they are able to reproduce. Considering
this, together with the results of Levitin (1994) and other
studies, we wonder (perhaps somewhat facetiously)
whether what people encode in memory is the first bar of
what would be written music, including the key, time sig-
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LEVITIN AND COOK
nature, and metronome marking! This would be parsimonious, allowing the brain to store only the temporal
and melodic relations between tones and imposing temporal and pitch anchors only when needed. And it would
explain the ease with which people are able to identify
transpositions of pitch and changes in tempo. But our
subjective impression, based on introspection, is that
long-term memory for music functions more like what
Attneave and Olson (1971) described as short-term music
memory:
The circulating short-term memory of a tonal sequence
just heard, which is experienced as an auditory image extended in real time (as a melody that “runs through one’s
head”), typically preserves the key or specific pitch values of the original. (p. 164)
Attneave and Olson (1971) believed that, in contrast,
the long-term memory trace is encoded only on the basis
of relations, or intervals. They note that there is nothing
about such a coding system that precludes the additional
storage of pitch or tempo information, “but it is evident
that normal individuals do not, in fact, preserve this kind
of information with any high degree of precision” (pp. 164–
165). We believe that the present study provides evidence against this point, and that ordinary individuals do
possess representations that are more accurate than has
previously been believed. Furthermore, the present study
provides evidence that the two types of operations present in musical listening—schematic reduction and unreducible idiostructural information (Narmour, 1977)—
appear to also be present in long-term memory.
REFERENCES
Allen, G. D. (1975). Speech rhythm: Its relation to performance universals and articulatory timing. Journal of Phonetics, 3, 75-86.
Attneave, F., & Olson, R. K. (1971). Pitch as a medium: A new approach to psychophysical scaling. American Journal of Psychology,
84, 147-166.
Block, R. A. (Ed.) (1990). Cognitive models of psychological time.
Hillsdale, NJ: Erlbaum.
Boltz, M. G. (1994). Changes in internal tempo and effects on the
learning and remembering of event durations. Journal of Experimental Psychology: Learning, Memory, & Cognition, 20, 1154-1171.
Bower, G. H. (1967). A multicomponent theory of the memory trace.
In K. W. Spence & J. T. Spence (Eds.), The psychology of learning
and motivation: Advances in research and theory (Vol. 1, pp. 229325). New York: Academic Press.
Braun, F. (1927). Untersuchungen über das persönliche tempo [Investigations into personal tempo]. Archiv der gesamten Psychologie, 60, 317-360.
Brooks, L. R. (1978). Nonanalytic concept formation and memory for
instances. In E. Rosch & B. B. Lloyd (Eds.), Cognition and categorization (pp. 169-211). Hillsdale, NJ: Erlbaum.
Collier, G. L., & Collier, J. L. (1994). An exploration of the use of
tempo in jazz. Music Perception, 11, 219-242.
Collier, G. L., & Wright, C. E. (1995). Temporal rescaling of simple and complex ratios in rhythmic tapping. Journal of Experimental Psychology: Human Perception & Performance, 21, 602-627.
Collyer, C. E., Broadbent, H. A., & Church, R. M. (1994). Preferred rates of repetitive tapping and catagorical time production.
Perception & Psychophysics, 55, 443-453.
Crowder, R. G., Serafine, M. L., & Repp, B. (1990). Physical interaction and association by contiguity in memory for the words and
melodies of songs. Memory & Cognition, 18, 469-476.
Dennett, D. C. (1991). Consciousness explained. Boston: Little,
Brown.
Desain, P. (1992). A (de)composable theory of rhythm perception.
Music Perception, 9, 439-454.
Deutsch, D. (1991). The tritone paradox: An influence of language
on music perception. Music Perception, 8, 335-347.
Dowling, W. J., & Bartlett, J. C. (1981). The importance of interval information in long-term memory for melodies. Psychomusicology, 1, 30-49.
Drake, C., & Botte, M.-C. (1993). Tempo sensitivity in auditory sequences: Evidence for a multiple-look model. Perception & Psychophysics, 54, 277-286.
Finke, R. A. (1985). Theories relating mental imagery to perception.
Psychological Bulletin, 98, 236-259.
Fraisse, P. (1981). Rhythm and tempo. In D. Deutsch (Ed.), The psychology of music (pp. 149-180). New York: Academic Press.
Friberg, A., & Sundberg, J. (1993). Perception of just noticeable
time displacement of a tone presented in a metrical sequence at different tempos. In Kungliga Tekniska Högskolan, Speech Transmission Laboratory [Eds.], Quarterly progress and status report
(pp. 49-55). Stockholm: Royal Institute of Technology, Department
of Speech Communication, Speech Transmission Laboratory.
Gilden, D. L., Thornton, T., & Mallon, M. W. (1995, March 24). 1/f
noise in human cognition. Science, 272, 1837-1839.
Halpern, A. R. (1988). Perceived and imagined tempos of familiar
songs. Music Perception, 6, 193-202.
Halpern, A. R. (1989). Memory for the absolute pitch of familiar
songs. Memory & Cognition, 17, 572-581.
Halpern, A. R. (1992). Musical aspects of auditory imagery. In
D. Reisberg (Ed.), Auditory imagery (pp. 1-28). Hillsdale, NJ: Erlbaum.
Hanson, H. M. (1959). Effects of discrimination training on stimulus
generalization. Journal of Experimental Psychology, 58, 331-334.
Helmuth, L. L., & Ivry, R. B. (1996). When two hands are better than
one: Reduced timing variability during bimanual movements. Journal of Experimental Psychology: Human Perception & Performance,
22, 278-293.
Hibi, S. (1983). Rhythm perception in repetitive sound sequence.
Journal of the Acoustical Society of Japan, 4, 83-95.
Hintzman, D. L. (1986). “Schema abstraction” in a multiple-trace
memory model. Psychological Review, 93, 411-428.
Hulse, S. H., Fowler, H., & Honig, W. K. (Eds.) (1978). Cognitive
processes in animal behavior. Hillsdale, NJ: Erlbaum.
Hulse, S. H., & Page, S. C. (1988). Toward a comparative psychology
of music perception. Music Perception, 5, 427-452.
Hurly, T. A., Ratcliffe, L., & Weisman, R. (1990). Relative pitch
recognition in white-throated sparrows, Zonotrichia albicollis. Animal Behavior, 40, 176-181.
Ivry, R. B., & Hazeltine, R. E. (1995). The perception and production of temporal intervals across a range of durations: Evidence for
a common timing mechanism. Journal of Experimental Psychology: Human Perception & Performance, 21, 3-18.
Jacoby, L. L. (1983). Remembering the data: Analyzing interaction
processes in reading. Journal of Verbal Learning & Verbal Behavior, 22, 485-508.
Jones, M. R., & Boltz, M. (1989). Dynamic attending and responses
to time. Psychological Review, 96, 459-491.
Konishi, M., & Kenuk, A. S. (1975). Discrimination of noise spectra
by memory in the barn owl. Journal of Comparative Physiology,
97, 55-58.
Kosslyn, S. M. (1980). Image and mind. Cambridge, MA: Harvard.
Kuhn, T. L. (1974). Discrimination of modulated beat tempo by professional musicians. Journal of Research in Music Education, 22,
270-277.
Kuhn, T. L. (1977). Effects of dynamics, halves of exercise, and trial
sequences on tempo accuracy. Journal of Research in Music Education, 25, 222-227.
Levitin, D. J. (1994). Absolute memory for musical pitch: Evidence
from the production of learned melodies. Perception & Psychophysics, 56, 414-423.
Lockhead, G. R., & Byrd, R. (1981). Practically perfect pitch. Journal of the Acoustical Society of America, 70, 387-389.
MEMORY FOR TEMPO
McClelland, J. L., & Rumelhart, D. E. (1986). A distributed model
of human learning and memory. In D. E. Rumelhart, J. L. McClelland, & the PDP Research Group (Eds.), Parallel distributed processing: Vol. 2. Psychological and biological models (pp. 170-215).
Cambridge, MA: MIT Press.
Medin, D. L., & Schaffer, M. M. (1978). Context theory of classification learning. Psychological Review, 85, 207-238.
Michon, J. A., & Jackson, J. L. (Eds.) (1985). Time, mind, and behavior. New York: Springer-Verlag.
Monahan, C. B. (1993). Parallels between pitch and time and how
they go together. In T. J. Tighe & W. J. Dowling (Eds.), Psychology
and music: The understanding of melody and rhythm (pp. 121-154).
Hillsdale, NJ: Erlbaum.
Moore, B. C. J., & Glasberg, B. R. (1986). The relationship between
frequency selectivity and frequency discrimination for subjects
with unilateral and bilateral cochlear impairment. In B. C. J. Moore
& R. D. Patterson (Eds.), Auditory frequency selectivity (pp. 407414). New York: Plenum.
Narmour, E. (1977). Beyond Schenkerism: The need for alternatives
in music analysis. Chicago: University of Chicago Press.
Perron, M. (1994, November). Checking tempo stability of MIDI sequencers. Paper presented at the 97th Convention of the Audio Engineering Society, San Francisco.
Pitt, M. A. (1995). Evidence for a central representation of instrument timbre. Perception & Psychophysics, 57, 43-55.
Posner, M. I., & Keele, S. W. (1970). Retention of abstract ideas.
Journal of Experimental Psychology, 83, 304-308.
Povel, D. J. (1981). Interval representation of simple temporal patterns. Journal of Experimental Psychology: Human Perception & Performance, 7, 3-18.
Povel, D. J., & Essens, P. (1985). Perception of temporal patterns.
Music Perception, 2, 411-440.
Premack, D. (1978). On the abstractness of human concepts: Why it
would be difficult to talk to a pigeon. In S. H. Hulse, H. Fowler, &
W. K. Honig (Eds.), Cognitive processes in animal behavior
(pp. 423-451). Hillsdale, NJ: Erlbaum.
Reese, H. W. (1968). The perception of stimulus relations. New York:
Academic Press.
Rosch, E. (1975). Cognitive representations of semantic categories.
Journal of Experimental Psychology: General, 104, 192-223.
Serafine, M. L. (1979). A measure of meter conservation in music,
based on Piaget’s theory. Genetic Psychology Monographs, 99, 185229.
935
Snedecor, G. W., & Cochran, W. G. (1989). Statistical methods
(8th ed.). Ames, IA: Iowa State University Press.
Steedman, M. J. (1977). The perception of musical rhythm and metre.
Perception, 6, 555-570.
Terhardt, E., & Seewan, M. (1983). Aural key identification and its
relationship to absolute pitch. Music Perception, 1, 63-83.
Tooze, Z. J., Harrington, F. H., & Fentress, J. C. (1990). Individually distinct vocalizations in timber wolves, Canis lupus. Animal
Behavior, 40, 723-730.
NOTE
1. Only 88 data points are shown in Figures 1 and 2. We started with
46 subjects in Trial 1; 3 discontinued participation after Trial 1, and
we eliminated the data of one Trial 2 subject. This Trial 2 subject
asked to sing a Mozart piano sonata on Trial 2, complaining that she
didn’t know any rock songs other than her Trial 1 choice (“Hey Jude”).
The experimenter let her sing the piano sonata. Later, during the
analysis phase of the study, we realized that multiple recorded versions of such a piece exist, and virtually all are in the same key, so this
subject’s production was not excluded from the original pitch analysis reported in Levitin (1994). However, the range of tempos over
which such pieces are performed typically varies, so this subject was
excluded in the tempo analysis, on the ground that a single reference
standard did not exist.
2. The low correlation between pitch memory and tempo memory
could indicate that subjects have either independent storage or integrated storage of these two attributes, in the sense of the terms proposed by Crowder, Serafine, and Repp (1990). In independent storage,
memory for one element is uninfluenced by the other; in integrated
storage, the elements are related in memory in such a way that one
component is better recognized in the presence of the other than in its
absence. The present data do not provide direct evidence for choosing
between these two possibilities, but it is our intuition that tempo and
pitch are best characterized by an integrated storage account. Some
subjects are able to recall both attributes with great accuracy (one attribute might indeed aid the accurate recall of the other) while other
subjects showed no such benefit.
(Manuscript received July 11, 1995;
revision accepted for publication December 14, 1995.)